Long-time stable and high-performance YBa₂Cu₃O₇ nanoSQUIDs with more interfaces Open Access

Within the rapidly developing field of nanoscale science and technology, nanomagnetism has emerged as a highly attractive discipline, due to intriguing basic physical phenomena¹ that are accompanied by a wide range of potential applications, from spintronic devices and ultra-high-density data-storage media for (quantum) information technologies through magnetic fluids for industrial use, up to biotechnology applications, including enhanced imaging of tissue and organs, virus-detecting magnetic resonance imaging, and cancer therapy.² 

SQUIDs (superconducting quantum interference devices) are macroscopic quantum objects that are capable of measuring a wide range of physical parameters with unequaled sensitivity.^3–8 Miniaturized direct current (dc) superconducting quantum interference devices (SQUIDs) with dimensions in the submicrometer range (nanoSQUIDs) are promising devices for sensitive detection and investigation of small spin systems.^9–17 YBa₂Cu₃O₇ (YBCO) nanoSQUIDs^18–20 with by far the lowest flux noise in the thermal white noise limit are based on bicrystal grain boundary Josephson junctions (GBJJs). Furthermore, YBCO nanoSQUIDs have a much wider temperature range of operation (from mK to above 77 K)^21–24 compared to their low critical temperature superconductor (LTS) counterparts^25,26 greatly simplifying their practical applications. More importantly, the cuprate superconductor YBCO offers SQUIDs operation up to much higher magnetic field, due to the huge upper critical field of at least tens of tesla, which is necessary for the investigation of magnetic nanoparticles.

However, the superconducting coherence length is very short and anisotropic of the YBCO material, typically around 2 nm in the a–b plane and 0.2 nm along the c axis. Due to the complex nature of these materials, and, in particular, their small coherence length associated with strong sensitivity to defects on the atomic scale, a major challenge is their chemical instability and oxygen diffusion, especially at lateral sizes down to the 100-nm range, which can lead to serious degradation of their properties.²⁷ To avoid degradation is essential since the long-term sensor stability is a requirement for the application of high-temperature nanoSQUIDs. However, YBCO nanoSQUIDs degrade quickly if the samples are stored at room temperature. This hampers the production efficiency and a more widespread use of nanoSQUIDs, e.g., if we want to send them to other groups for placing magnetic nanoparticles (MNPs) on top of our nanoSQUIDs. A possible cause for the degradation of superconducting thin films is the diffusion of oxygen in the YBCO layer. In monocrystalline films, the oxygen transport occurs along the a–b plane of the crystals.²⁸ At growth defects or grain boundaries, a significant oxygen diffusion appears along the c axis of the epitaxially grown film.^29,30

To realize the long-term sensor stability, suitable insulating materials as the capping layers should be lattice-matched, smooth, dense, crack-free, and chemically inert for the growth of the YBCO multilayers while also transferring the biaxial texture to the newly deposited layers. Several coating materials, such as polyimide, Nb₂O₅, Al₂O₃, amorphous YBCO, and SiO₂, have been studied.^31–35 Most of these capping layers degrade T_c and the critical current density J_c of the YBCO thin films. SrTiO₃ (STO) has been proven to be a good candidate for insulating YBCO layers in multi-layered architecture.³⁶ 

In this paper, long-time stable and high-performance YBCO nanoSQUIDs with more YBCO/STO interfaces have been demonstrated, which is beneficial to the production efficiency and a more widespread use of nanoSQUIDs. There are two functions of YBCO/STO periodic structure. First, the STO layer can act as the capping layer, which can avoid degradation of the hygroscopic surface in air and significant oxygen diffusion appears along the c axis of the epitaxially grown film after focus ion beam milling. Second, the multi-layered structure can provide extra heteroepitaxial interfaces to interrupt the defect growth, which is consistent with lower 1/f noise in bicrystal GBJs compared with single layer YBCO nanoSQUIDs.

The schematic view of YBCO/STO nanoSQUID is illustrated in Fig. 1. A c axis oriented YBCO thin film with thickness around 30 nm is grown epitaxially on an STO bicrystal substrate with a misorientation angle 2θ = 24° (θ = 12°). Next, a 3 nm STO thin film is deposited with the same deposition parameters. Then, the same process continued until 120 nm YBCO thin film in total with three interlayer STO between YBCO films is developed. An in situ evaporated Au layer with a thickness of 65 nm serves as the shunt resistance to provide nonhysteretic current–voltage characteristics (IVCs). After optical lithography and argon milling process, 16 junctions with 8 μm width are grown on the surface of the STO bicrystal. YBCO nanoSQUIDs with similar sizes are fabricated by using the focused-ion-beam (FIB) with 30-keV Ga⁺ ions.

Regarding the characterization, the in-plane grain orientation of the YBCO film is investigated by using x-ray diffraction (XRD) ϕ-scans (PhilipsX’Pert diffraction system). For characterization of the device properties, electric transport and noise measurements are performed in an electrically and magnetically shielded environment at T = 4.2 K, i.e., with the samples immersed into liquid helium. By applying a modulation current I_mod across the constriction, the magnetic flux coupled to the SQUID can be modulated. This scheme allows flux biasing at the optimum working point and operation in a flux-locked loop (FLL) mode.³⁷ 

In this section, we present and discuss electric transport and noise properties measured in liquid helium at T = 4.2 K in an electrically and magnetically shielded environment. We focus on two fabricated YBCO/STO superlattice nanoSQUIDs, SQ-14 and SQ-15, which were FIB-patterned from JJ-14 and JJ-15, respectively. For comparison, we also show the data for a single layer YBCO nanoSQUID (SQ-SL) with comparable geometry, which was FIB patterned from JJ-SL, also on an STO bicrystal substrate. The summary of geometric and electric parameters of nanoSQUIDs is shown in Table I, where W_J1 and W_J2 describe the width of two Josephson junctions formed into nanoSQUID, W_c and L_c represent the width and length of constriction, respectively, and L_J is the length of Josephson junction formed into nanoSQUID.

To estimate the values of T_c, an inductive method based on the change of the behavior (inductance) of a coil caused by the change of magnetic permeability of the YBCO inside the coil is used. Figure 2 presents the inductive T_c measurement for three samples with the thickness of 7.3, 16.6, and 23 nm on a single STO substrate. It is obvious to note that the YBCO superconductivity is depressed if the film thickness is less than a few nanometers. In particular, a deficient oxygenation of YBCO and interface disorder, strain, or interdiffusion could cause the superconductivity depression. The epitaxial mismatch strain is known to cause deep structural modifications, which have been proposed as a source of superconductivity depression in the cuprate superconductors. In other words, each layer with film thickness down to a few nanometers is not a good option if we want to achieve good superconductivity.

However, the roughness of YBCO films obtained by using pulsed laser deposition (PLD) is a well-known problem especially when the film thickness becomes thicker. In order to take the advantages of superconductivity and surface tomography, 30 nm YBCO and 3 nm STO as one period is desired.

Figure 3(a) shows the SEM image of the chip 2 SQUID 15. The two bridges straddling the grain boundary have a width around 250 nm. The right part of the SQUID loop contains a constriction with width of about 250 nm. An applied bias current I_b flows from right to left across the two GBJs, and the modulation current flows through the constriction as the magnetic flux coupled into SQUID hole. It is clear to note that the surface topography is the same without obvious degradation after 45 days in air, which is not the case for single layer YBCO nanoSQUIDs. In this case, YBCO nanoSQUIDs with more interfaces are helpful in avoiding surface topography degradation in air.

Figure 4(a) shows IVCs of SQUID 15 at t = 1 d for two values of I_mod yielding maximum critical current I_c,max = 287 μA and minimum critical current I_c,min = 123 μA and normal resistance R_n = 1.3 Ω. This results in a characteristic voltage V_c = I_c,maxR_n = 373 μV, which is comparable to GBJJ nanoSQUIDs from single layer YBCO films with similar geometry.

Figure 5 illustrates the critical current I_c vs I_mod, recorded at different times t (from t = 1 to 213 days). It is clear that the critical current drops by 30% from I_c = 287 μA to I_c = 200 μA after 39 d. From the modulation period I_mod,0, we determine the mutual inductance M = Φ₀/I_mod,0 = 0.95 pH, where Φ₀ is the magnetic flux quantum. The minimum critical current I_c,min is less than 50% of I_c,max. From the approximate relation for the modulation depth (I_c,min − I_c,max)/I_c,max ≈ 1/(1 + β_L), we estimate a screening parameter β_L ≡ LI_c,max/Φ₀ slightly below 0.5 and from this, a SQUID inductance L ∼ 5 pH. The decrease of I_c with t slows down, as shown by further measurements at t = 130 and 213 d. Except that, it is clear to see the shift of the current modulation with time. More accurate estimates of parameters such as β_L and L and asymmetry parameters α_I and α_L need further investigation.

In the following, we discuss two YBCO/STO multilayer nanoSQUIDs (SQUID 14 and 15) and, for comparison, one YBCO single layer nanoSQUID (SQUID 2). For the multilayer SQUID 14, the critical current drops fast within the first 39 days and then remains constant in time, even up to 380 days. A similar trend is also observed for the multilayer SQUID 15. For comparison, Fig. 6(c) shows IVCs of the single layer SQUID 2, measured after 1 day and 350 days. Clearly, no critical current can be detected after 350 days. In fact, we checked several single layer SQUIDs and none of them showed a finite critical current after 350 days. In this case, long-time stability of YBCO nanoSQUIDs with more interfaces can be actualized.

Figures 7(a)–7(d) show V − I_mod oscillations, measured with different bias currents after 1 day, 39 days, 130 days, and 213 days, respectively. The devices show nonhysteretic IVCs and continuous V − I_mod oscillations. Hence, a nonhysteretic SQUID can be considered as a magnetic flux to voltage transducer and can be employed as a magnetic flux detector. Typically, in this configuration, the SQUID is biased with a constant current close to I_c and an external magnetic flux Φ_e = 0.25 Φ₀ in order to maximize the voltage responsivity, namely, the slope of the V − Φ curve in the magnetic bias point, and increase the Signal to Noise Ratio (SNR). It is clear to see that the function of YBCO nanoSQUID is still excellent even up to 213 days in air.

Finally, we discuss the flux noise of the YBCO nanoSQUIDs with more YBCO/STO interfaces, which has been measured in the FLL mode. Figure 8 shows the root-mean-square (rms) spectral density of flux noise of SQ-15 measured with dc bias.^38–41 The rms flux noise for both SQUIDs at the lowest frequency of 1 Hz is very similar, around 5–6 µΦ₀/Hz^1/2 with dc bias. For comparison, typical single layer YBCO GBJJ SQUIDs on bicrystal STO show 100 µΦ₀/Hz^1/2 at 1 Hz. Regarding time dependence, Fig. 8 shows the rms spectral density of flux noise of SQUID 15 measured at different times (t = 1, 39, and 89 d). Clearly, we observe no degradation of the low-frequency excess noise (at 1 Hz) even after 89 days. In fact, the data obtained in the bias reversal mode yield a significant improvement of flux noise at 1 Hz. This shows that I_c fluctuations are the major source of low-frequency excess noise in our devices. Hence, we conclude that the lower low-frequency excess noise in the YBCO nanoSQUIDs with more interfaces is most likely due to an improved quality of the grain boundary, as compared to single layer YBCO nanoSQUIDs. In view of these observations, we demonstrate that long-time stable and high-performance of YBCO nanoSQUIDs with more interfaces is plausible.

We have successfully fabricated YBCO/STO nanoSQUIDs on a bicrystal STO substrate with 24° misorientation angle. Based on the electronic measurement with the time span more than one year, we confirm that long-time stable and high-performance YBCO nanoSQUIDs can be realized in this YBCO/STO periodic structure, which pave the way for better operation and provide insights into some other nanoelectronic devices. Two functions of YBCO/STO periodic structure have been demonstrated. First, the STO layer can act as the capping layer, which can avoid the degradation of the hygroscopic surface in air and significant oxygen diffusion appears along the c axis of the epitaxially grown film. Second, the lower low-frequency excess noise in the YBCO nanoSQUIDs with more interfaces is most likely due to an improved quality of the grain boundary, as compared to single layer YBCO nanoSQUIDs. To exploit the potential of the multilayer periodic structure technology, the designs can be further developed considering the applications in magnetometry, susceptometry, and read-out of other nanoscale devices.

We thank M. Turad, R. Loeffler (LISA+), D. Koelle, R. Kleiner, and C. Back for fruitful discussions and technical support. This work was supported by the COST action NANOCOHYBRI (Grant No. CA16218), the National Natural Science Foundation of China (Grant No. 12104112), and the Natural Science Foundation of Shandong Province (Grant No. ZR2021QA036).

The authors have no conflicts to disclose.

The data that support the findings of this study are available within the article.